Fisher Information Measure Research Articles

Comparing the Efficiency and Similarity Between WTI, Fiat Currencies and Foreign Exchange Rates

The complex dynamics of financial asset prices play a pivotal role in the global economy and consequently in the life of the people. Thus, this research encompasses a systematic analysis of the price dynamics of the financial assets considering simultaneously four critical attributes of the financial market (disorder, predictability, efficiency and similarity/dissimilarity). We explore these essential attributes of the financial market using the permutation entropy ([Formula: see text]) and Fisher Information measure ([Formula: see text]), and cluster analysis. Primary, we use the values of the information theory quantifiers to construct the Shannon–Fisher causality plane (SFCP) allows us to quantify the disorder and assess the randomness exhibited by these financial price time series. Bearing in mind the complexity hierarchy, we apply the values of [Formula: see text] and [Formula: see text] to rank the efficiency of these financial assets. The overall results suggest that the fiat currencies of developed countries, such as the Canadian dollar (CAD), British pound (GBP), and Norwegian krone (NOK), display higher disorder, lower predictability, and higher efficiency than other financial assets such as Crude oil (WTI) and Foreign exchange rates. Also, the cluster analysis provided by the K-means and the Hierarchical cluster techniques grouped these financial assets into only three distinct groups. We conclude that an oligopolistic market structure drives the WTI. At the same time, the other financial assets are characterized by atomized markets.

The resilience of cryptocurrency market efficiency to COVID-19 shock

We examine the price disorder and informational efficiency of five cryptocurrencies (Bitcoin, BNB, Cardano, Ethereum, and XRP) before and during the COVID-19 pandemic. In this sense, we estimate the permutation entropy and Fisher information measure (FIM). We use these complexity measures to construct the Shannon–Fisher causality plane (SFCP) to map these cryptocurrencies and their respective locations in a two-dimensional plane and then apply the sliding time window approach to study the temporal evolution of informational efficiency. All cryptocurrencies exhibit high but slightly varying informational efficiency during both periods. Cardano was the most efficient cryptocurrency. These results might point to the increasing maturity and lower potential for price predictability, which matter to cryptocurrencies’ usage for liquidity risk diversification strategy.

Booms in commodities price: Assessing disorder and similarity over economic cycles

This paper provides an overview of the commodities market, considering three relevant attributes: predictability, similarity, and efficiency. We examine the monthly spot and futures prices time series for 22 commodities from January 1984 until January 2022 with 457 observations. We estimate the permutation entropy (Es) and Fisher information measure Fs using the Bandt & Pompe method (BPM). We employ the value of these two complexity measures to construct the Shannon–Fisher Causality Plane (SFCP), which allows us to evaluate the disorder and assess the randomness present in the monthly spot and futures prices time series for these commodities. Moreover, we apply Es and Fs to classify the commodities using complexity hierarchy. We find that the commodities that are located farther from the random ideal position (Es=1,Fs=0) in the SFCP, such as Natural gas, Europe; Iron ore, cfr spot, and Potassium chloride are marked by lower entropy, higher predictability and lower efficiency. In contrast, the commodities that are located near the random ideal position (Es=1,Fs=0) in the SFCP, such as Crude oil-Brent; Crude oil-average, and Silver are characterized by higher entropy, lower predictability and higher efficiency. The K-means algorithm and the hierarchical cluster grouped commodities into only three distinct groups, which is a strong indication that commodity prices have very similar behavior.

ECG Signals Classification Using Overlapping Variables to Detect Atrial Fibrillation

In the present work a method for the detection of the cardiac pathology known as atrial fibrillation is proposed by calculating different information, statistics and other nonlinear measures over ECG signals. The original database contains records corresponding to patients who are diagnosed with this disease as well as healthy subjects. To formulate the dataset the Rényi permutation entropy, Fisher information measure, statistical complexity, Lyapunov exponent and fractal dimension were calculated, in order to determine how to combine this features to optimize the identification of the signals coming from ECG with the above mentioned cardiac pathology. With the aim to improve the results obtained in previous studies, a classification method based upon decision trees algorithms is implemented. Later a Montecarlo simulation of one thousand trials is performed with a seventy percent randomly selected from the dataset dedicated to train the classifier and the remaining thirty percent reserved to test in every trial. The quality of the classification is assessed through the computation of the area under the receiver operation characteristic curve (ROC), the F1-score and other classical performance metrics, such as the balanced accuracy, sensitivity, specificity, positive and negative predicted values. The results show that the incorporation of all these features to the dataset when are employed to train the classifier in the training task produces the best classification, in such a way that the largest quality parameter is achieved.

Cumulative past Fisher information measure and its extensions

In this work, we define the cumulative past Fisher (CPF) information and the relative cumulative past Fisher (RCRF) information measures for parameter as well as for the distribution function of the underlying random variables. We show that these cumulative past Fisher information measures can be expressed in terms of the reversed hazard rate function. We also define three extensions of the CPF information measure. Further, we study these cumulative information measures and their Bayes versions for some well-known models used in reliability, economics and survival analysis. The associated results reveal some interesting connections between the proposed Fisher type information measures with some well-known information divergences and reliability measures.

Analytical Solutions of the Klein-Gordon equation and Fisher information with Inversely Quadratic Hellman potential

The inversely quadratic Hellman (IQH) potential has gained recognition in recent times. This paper is focused on the analytical solutions of the Klein-Gordon equation with the IQH potential and its application to Fisher information. Using the parametric form of the Nikiforov-Uvarov method, the relativistic and non-relativistic energies of the IQH potential are obtained, along with the wave functions. Furthermore, the Fisher information measure and uncertainty of the system are obtained. Our results show that the momentum space probability density function is more localized. This is confirmed to be true by the high values of the Fisher information in momentum space. Furthermore, the occurrence of squeezed states is observed. The uncertainty results and the Fisher information show that the system is stable.

AN ANALYSIS OF THE PREDICTABILITY OF BRAZILIAN INFLATION INDEXES BY INFORMATION THEORY QUANTIFIERS

This research explores the predictability of the Brazilian inflation monthly price indexes time series by information theory quantifiers. Given this, we apply the Bandt and Pompe method to estimate the information theory quantifiers, specifically the Permutation entropy ([Formula: see text]) and the Fisher information measure ([Formula: see text]). Based on the values of both complexity measures, we construct the 2D plane called the Shannon-Fisher causality plane, which allows us to explore the disorder and quantify the randomness inherent to the temporal evolution of the significant Brazilian inflation indexes. Also, we apply [Formula: see text] and [Formula: see text] to rank the Brazilian inflation indexes based on the complexity hierarchy. An overview shows that the Brazilian inflation indexes display lower entropy which implies in higher predictability. The sliding window approach reveals that Brazilian inflation indexes (IPA, IPCA, IGP, IPC, and INPC) present decrease related to efficiency. The only exception is the INCC, which shows an increase in efficiency.

LIGHTING THE POPULATIONAL IMPACT OF COVID-19 VACCINES IN BRAZIL

This paper examines the populational impact of the COVID-19 vaccinations for Brazil. Therefore, our analysis takes into account the time series of the daily number of deaths related to COVID-19 from March 17, 2020 until October 19, 2021 with 582 observations. Specifically, we apply the permutation entropy ([Formula: see text]), statistical complexity ([Formula: see text]) and Fisher information measure ([Formula: see text]) to investigate the predictability of the daily deaths for COVID-19 considering two pandemic scenarios (until and after the extreme day). Based on these complexity measures, we construct the Complexity-Entropy causality plane (CECP) and Shannon–Fisher causality plane (SFCP), which allows us to assess the disorder and estimate randomness inherent to the time series of the daily deaths for COVID-19 concerning these two pandemic scenarios. Our empirical results indicate that after the extreme day, the increase in the vaccinated population contingent led to a lower entropy, higher predictability, and lower death cases. Given this, we conclude that the COVID-19 vaccines in Brazil were a highly effective public health action. In the most extreme situation, Brazil had 4249 records of daily deaths on April 8, 2021, approximately 3.5 months after the first dose of the vaccine. After this extreme situation on April 9, 2021, the daily records of deaths decrease to a minimum of 130 deaths on October 19, 2021. Thus, there is a percentage variation of −96.44% in records of daily deaths. To the best of our knowledge, this work is the first to provide empirical evidence for the populational impact related to COVID-19 vaccines.

Generating function for generalized Fisher information measure and its application to finite mixture models

Generating function for generalized Fisher information measure and its application to finite mixture models

Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures.

In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic function as a new extension of hazard rate function. We show that CRQF information measure can be expressed in terms of the QHR function. We define further generalized cumulative residual divergence measures between two SFs. We then examine the cumulative residual q-Fisher information for two well-known mixture models, and the corresponding results reveal some interesting connections between the cumulative residual q-Fisher information and the generalized cumulative residual divergence measures. Further, we define Jensen-cumulative residual (JCR-) measure and a parametric version of the Jensen-cumulative residual Fisher information measure and then discuss their properties and inter-connections. Finally, for illustrative purposes, we examine a real example of image processing and provide some numerical results in terms of the CRQF information measure.

Exploiting the impact of ordering patterns in the Fisher-Shannon complexity plane

The Fisher-Shannon complexity plane is a powerful tool to characterize complex dynamics. It locates, on a two-dimensional plane, a dynamical system based upon its entropy and its Fisher Information Measure (FIM). It has been recently shown that by using ordinal patterns to compute permutation entropy and FIM, this plane unveils inner details of the structure underlying the complex and chaotic dynamics of a system, not easily exposed by other methods. The entropy of the dynamics is invariant to the way the patterns are ordered, but the way FIM is defined is sensitive to the order in which we classify the ordinal patterns. In this paper we analyze in detail the impact that the sorting protocol used to calculate FIM has on the structure unveiled by the Fisher-Shannon plane. We show the importance of a suitable choice, which can lead to saving computational resources, but also to disclose details of the dynamics not accessible to other sorting protocols. Our results agree with previous research, and common characteristic fingerprints are found for the different chaotic maps studied. Our analysis also reveals the fractal behaviour of the chaotic maps studied. We extract some underlying symmetries that allow us to simulate the behaviour on the complexity plane for a wide range of the control parameters in the chaotic regimes.

INSIGHTS INTO THE PREDICTABILITY AND SIMILARITY OF COVID-19 WORLDWIDE LETHALITY

This paper performs a systematic investigation into the temporal evolution of daily death cases of COVID-19 worldwide lethality considering 90 countries. We apply the information theory quantifiers, more specifically the Permutation entropy [Formula: see text] and Fisher information measure [Formula: see text] to construct the Shannon-Fisher causality plane (SFCP), which allows us to quantify the disorder and evaluate randomness present in the time series of daily death cases related to COVID-19 in each country. Moreover, we employ [Formula: see text] and [Formula: see text] to rank the COVID-19 lethality in these countries based on the complexity hierarchy. Our findings reveal that the countries that are located farther from the random ideal position ([Formula: see text], [Formula: see text]) in the SFCP such as Taiwan, Vietnam, New Zealand, Singapore, Monaco, Iceland, Thailand, Bahamas, Cyprus, Australia, and Norway are characterized by a less entropy and low disorder, which leads to high predictability of the COVID-19 lethality. Otherwise, the countries that are located near to the random ideal position ([Formula: see text], [Formula: see text]) in the SFCP such as Ecuador, Czechia, Iraq, Colombia, Belgium, Italy, Philippines, Iran, Peru, and Japan are characterized by high entropy and high disorder, which implies low predictability of the COVID-19 lethality. We also employ two cluster techniques to analyze the similarity considering the temporal evolution of COVID-19 worldwide lethality for the countries investigated. Based on the values of [Formula: see text], [Formula: see text] and our cluster analysis, we suggest that this health crisis will only be adequately combated through global adherence to scientific exchange and technology sharing to homogenize the actions to combat the COVID-19.

Cumulative Residual and Relative Cumulative Residual Fisher Information and Their Properties

In this work, we propose cumulative residual Fisher information and relative cumulative residual Fisher information measures and establish some of their properties. We first show that these cumulative Fisher measures can be expressed based on the hazard function. We then define extended versions of cumulative residual entropy and cumulative residual Fisher information measures based on the Jensen inequality. We also discuss connections between these information measures based on a new version of de Bruijn's identity for survival functions.

Predictability of COVID-19 worldwide lethality using permutation-information theory quantifiers

This paper examines the predictability of COVID-19 worldwide lethality considering 43 countries. Based on the values inherent to Permutation entropy (Hs) and Fisher information measure (Fs), we apply the Shannon-Fisher causality plane (SFCP), which allows us to quantify the disorder an evaluate randomness present in the time series of daily death cases related to COVID-19 in each country. We also use Hs and Fs to rank the COVID-19 lethality in these countries based on the complexity hierarchy. Our results suggest that the most proactive countries implemented measures such as facemasks, social distancing, quarantine, massive population testing, and hygienic (sanitary) orientations to limit the impacts of COVID-19, which implied lower entropy (higher predictability) to the COVID-19 lethality. In contrast, the most reactive countries implementing these measures depicted higher entropy (lower predictability) to the COVID-19 lethality. Given this, our findings shed light that these preventive measures are efficient to combat the COVID-19 lethality.

Bound state solutions, Fisher information measures, expectation values, and transmission coefficient of the Varshni potential

The eigensolutions of the Schrödinger equation under the Varshni potential function are studied with two eigensolution techniques such as the Nikiforov–Uvarov and the semi-classical WKB approximation methods. We extended the work to investigate the analytical and numerical Fisher information measure of complexities and also the expectations values using the Hellmann–Feynman theorem. We determined the transmission coefficient using the WKB method. The WKB energy levels and mean values fluctuate with the potential range compared with the NU derived values. Our results for the Fisher information measure obey the uncertainty relation and the Cramer–Rao inequality for position space (). The mean values conform to the ones reported in existing literature.

Discrete Versions of Jensen-Fisher, Fisher and Bayes-Fisher Information Measures of Finite Mixture Distributions.

In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback–Leibler, Jeffreys and Jensen–Shannon divergences.

Complexity entropy-analysis of monthly rainfall time series in northeastern Brazil

In this work we analyze predictability and complexity of monthly rainfall temporal series recorded from 1950 to 2012, at 133 gauging stations in Pernambuco state, northeastern Brazil. To this end we use the complexity entropy causality plane (CECP) and Fisher Shannon plane (FS) formed by information quantifiers permutation entropy, permutation statistical complexity, and Fisher information measure, which serve to evaluate randomness and structural organization of the underlying process. By comparing the locations of analyzed stations in CECP and FS and performing statistical significance test, we distinguish rainfall regime in the deep inland, drier Sertão region, from the intermediate inland Agreste, and coastal, tropical humid Zona da Mata regions. We also perform time dependent CECP and FS analysis and for Sertão region identify the periods of higher entropy (lower complexity and Fisher information measure) which are related to El Niño episodes and historical droughts in northeastern Brazil. Our work represents a contribution to establishing the use of information theory based methods in climatological studies.

COVID-19 lethality in Brazilian States using information theory quantifiers

In this paper, we presented an overview diagnosis consider the time series of daily deaths by COVID-19 in the Brazilian States using Bandt & Pompe method (BPM) to estimate the Information Theory quantifiers, more specifically the Permutation entropy (H s ) and the Fisher information measure (F s ). Based on the Information Theory quantifiers, we build up the Shannon-Fisher causality plane (SFCP) to promote insights into the COVID-19 temporal evolution inherent in the phenomenology associated with the number of daily deaths well as their respective locations along the SFCP. Moreover, we apply H s and F s to elaborate on the rank of the Brazilian States’ real situation, considering the number of daily death due to COVID-19 based on the complexity hierarchy. The Brazilian States that are located in the middle region of the two-dimensional plane (H s x F s ), such as Amapá (AP), Roraima (RO), Acre (AC), and Tocantins (TO) are characterized by a less entropic and low disorder, which implies in high predictability of the COVID-19 lethality. While, the Brazilian States that are located in the lower-right region, such as Ceará (CE), Bahia (BA), Pernambuco (PE), and Rio de Janeiro (RJ), are characterized by high entropy and high disorder, which leads to low predictability of the COVID-19 lethality. Given this, our results provide empirical evidence that the permutation entropy is a powerful approach to predicting infectious diseases. Dynamic monitoring of permutation entropy can help policymakers to take more or less restrictive measures to combat COVID-19.

Fisher Shannon analysis of drought/wetness episodes along a rainfall gradient in Northeast Brazil

AbstractWe applied the informational approach of the Fisher‐Shannon method to study the time series of Standardized Precipitation Index (SPI) derived from monthly rainfall data at 133 gauging stations in Northeast (NE) Brazil. The climate in the study region ranges from tropical humid in the coastal area Zona de Mata to tropical semiarid inland Sertão, passing through a sub‐humid transition region Agreste. The time span is from 1962 to 2012, and SPI was calculated for 1, 3, 6, and 12 ‐ month time scales. We calculate information quantifiers Shannon entropy power (SEP) and Fisher information measure (FIM) that quantify signal disorder and structural organization, respectively, and define its position in the Fisher Shannon plane (FS). We find that the SPI‐1 series that describes short term dry/wet conditions display a higher degree of organization (higher FIM) and a lower degree of disorder (lower SEP) than SPI's that describe medium and long term conditions (SPI‐3, SPI‐6, and SPI‐12). By analysing the spatial distribution of information quantifiers, we find that short term dry/wet conditions (SPI‐1) show the lowest disorder and highest organization degree in the deep inland Sertão region and highest disorder and lowest organization degree in the coastal Zona de Mata region, while long term conditions (SPI‐12) show the opposite trend. For medium‐term conditions (SPI‐3 and SPI‐6), the SEP is highest and FIM lowest in the transition sub‐humid Agreste region. Our findings indicate that information theory‐based methods, particularly FS have the potential to discriminate among different climatic regimes.

An analysis of Brazilian agricultural commodities using permutation – information theory quantifiers: The influence of food crisis

Abstract We analyze predictability of selected Brazilian agricultural commodity prices (cotton, sugar, coffee, soybean and cattle) during the period 1997–2018 which encompasses the periods of agricultural commodities prices spikes between 2007 and 2011. We use information theory based methods entropy-complexity plane (HC) and entropy –Fisher information plane (HF), where Shannon entropy, statistical complexity and Fisher information measure are calculated for empirical Brandt-Pompe probability distribution of ordinal patterns. We find that coffee market shows lowest predictability (highest efficiency), while pork market shows highest predictability (lowest efficiency). By analyzing temporal evolution of efficiency index derived from Shannon entropy and Fisher information measure we observe that coffee and soybeans price series exhibit high and stable informational efficiency for all analyzed period, the efficiency of sugar market shows steady increase, while the efficiency of cattle and cotton market first decreases (until the crisis) and then increases in the post crisis period.